why do the cores get brittle and fall apart?
is it because they are vibrating?

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The problem isn't so much with the cores themselves (they don't seem to get appreciably more brittle with time -- at least, in my experience). The main problem seems to be that they bind against the inside of the coil form (Wally notes that the teflon-like tape had degraded in the specimen he analyzed), so that you can't apply enough torque to turn the cores without breaking them.